Characteristics
Domain:
\((-\infty,6)\cup(6,\infty)\)Range:
\((-\infty,0)\cup(0,\infty)\)x-intercepts: None
y-intercepts:
\((0,-0.3)\)Vertical asymptote: x = 6
Horizontal asymptote: y = 0
Extreme points: None
Find the distance between the two points rounding to the nearest tenth
(-4, 2) and (3, 5)
Answer:
-8.66666666666666666666666666666666666
-9
Step-by-step explanation:
Calculate the area of this figure to the nearest hundredth. Use 3.14 to approximate pi
Answer:
49.12 ft^2
Step-by-step explanation:
We can add the areas of the two figures
We have a triangle
A = 1/2 bh
A = 1/2 (6)(8)
A = 24
We have 1/2 of a circle so find 1/2 of the area
A = 1/2 ( area of a circle)
= 1/2 ( pi r^2)
The diameter is 8 so the radius is 4
= 1/2 ( 3.14 * 4^2)
= 25.12
Add the areas together
24+25.12 = 49.12
Answer:
49.12 ft²
Step-by-step explanation:
Among all pairs of numbers whose sum is 24, find a pair whose product is as large as possible. Show the work(the steps)! Write an equation of the corresponding quadratic function. How parabola opens? What is the maximum product? Does this function has a maximum value or the minimum value? Explain. Graph the function and upload the image.
The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.
To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.
Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.
To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:
P(x) = x(24 - x)
This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.
The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.
To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.
Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.
So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.
Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.
To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]
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3. A pound of flour costs $12. How many ounces of flour can be purchased for $3.30?
With a pound of flour costing $12 and considering that there are 16 ounces in a pound, the cost per ounce is $0.75. Thus, for $3.30, you can purchase 4.4 ounces of flour.
To find out how many ounces of flour can be purchased for $3.30, we need to determine the cost of one ounce of flour.
Given that a pound of flour costs $12, we know that there are 16 ounces in a pound (since there are 16 ounces in 1 pound). So, the cost of one ounce of flour can be calculated as:
Cost of one ounce of flour = Cost of one pound of flour / Number of ounces in one pound
Cost of one ounce of flour = $12 / 16 ounces
Cost of one ounce of flour = $0.75
Therefore, the cost of one ounce of flour is $0.75.
To determine how many ounces of flour can be purchased for $3.30, we divide the total amount of money by the cost of one ounce of flour:
Number of ounces of flour = Total money / Cost of one ounce of flour
Number of ounces of flour = $3.30 / $0.75
Number of ounces of flour ≈ 4.4 ounce
Therefore, for $3.30, approximately 4.4 ounces of flour can be purchased.
In summary, with the given cost of $12 for a pound of flour, and knowing that there are 16 ounces in a pound, we find that one ounce of flour costs $0.75. Thus, for $3.30, approximately 4.4 ounces of flour can be purchased.
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A cylinder with a radius of 2 yd and a height of
3 yd.
Answer:
20 π
Step-by-step explanation:
The surface area of a cylinder is made up of 2 circles and its side.
To find the circles' areas, use the area formula for a circle: A = π.
Since our radius is 2 yd, we can substitute r = 2 into this formula.
A = π = 4π
Now remember, this is only the area of once circle. Multiply 4π by 2 to get the area of both circles: 8π.
Now we need to find the surface area of the side.
If we flatten it out, we can see that the side is actually a curled up rectangle.
The length is the circumference of the circle and the width is the height of the cylinder.
To find the circumference, use the circumference formula for a circle: C = 2πr.
Substitute r = 2 into the formula.
C = 2π2 = 4π
Now that we know that the length is 4π, we can multiply the length by the width to find the area of the cylinder's side.
l = 4π
w = 3
A = lw = 4π * 3 = 12π
Finally, we can add the areas of the circles and the side to get the total surface area.
8π + 12π = 20π
And that is your answer!
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can you please help me
3. To find the perimeter of a rectangle, use the equation , where P is the perimeter, l is the length and w is the width of the rectangle.
(a) A rectangular garden has a perimeter of 40 yd and a width of 5 yd. Use the equation and the replacement set to find the length of the garden. Show your work.
(b) A rectangular table top has a perimeter of 18.4 ft and a length of 6.75 ft. Use the equation and the replacement set to find the width of the table top. Show your work.
Answer:
a) 15yd
b)2.45ft
Step-by-step explanation:
P = perimeter, l=length and w = width of the rectangle
P = 2l+2w
a) 40 = 2l+2(5)
40 = 2l+10
30=2l
15=l
b) 18.4 = 2(6.75) + 2w
18.4 = 13.5+2w
4.9=2w
2.45=w
y - 7 = 3 help me pls
Answer:
The answer is in the link
Step-by-step explanation:
Brainliest pls
Which function has the graph shown?
OAY COS
B. y -cos.x
● C. yin x
D. y sin (x)
f
The trigonometric function on the graph is:
f(x)= -cos(x)
So the correct option is B.
Which function is the graphed one?Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.
Notice that:
sin(0)= 0
cos(0) = 1
So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:
f(x) = -cos(x)
That is the graphed function.
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Find the value of: (4/5)^1 A. 4/5 B. 1 C. 0 D. 16/25
Answer:
A. 4/5
Step-by-step explanation:
Answer:
4/5 (option a)
Step-by-step explanation:
by following the exponent rule of \(a^1 = a\), we know that
\((\frac{4}{5} )^1\) = \(\frac{4}{5}\)
So, the value of
\(\frac{4}{5}^{1}\) is 4/5
Phillip is competing in a race car competition. He drives 218.4 miles in 2.4 hours.
(a) What unit rate may be of interest here?
If he drives the car 218.4 miles in 2.4 hours. Then the speed of the car will be 91 miles per hour.
How to find the speed of an object?If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.
If the object traveled D distance in T units of time, then that object's speed will be given as
Speed = Distance traveled/Time taken
S = D/T
Phillip is competing in a race car competition.
He drives 218.4 miles in 2.4 hours.
Then the speed of the car will be
S = 218.4/2.4
S = 91 miles per hour
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solve for x please, will give braknliest
If possible, find AB, BA, and A2.
First product:
\(AB=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\begin{bmatrix}1&0\\0&1\end{bmatrix}=\begin{bmatrix}\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\end{bmatrix}=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\)
Notice how multiplying A by B produces A again, because B is an identity matrix.
The second product cannot be carried out because A has more columns that B has rows.
The third product also cannot be computed because A is not a square matrix.
there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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Fine the length of segment x.
Answer:
10
Step-by-step explanation:
12+4=16
16-6=10
easy
this leads us to a sturm-louiville problem in x. in each case the general solution in x is written with constants a and b
An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.
The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.
For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following
form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.
The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.
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11. What is the unknown number in
Sequence 2 in the chart?
Sequence Number
Sequence 1
Sequence 2
A 126
B 127
c 147
D 154
2 3 5
7
14 21 35 49
?
1
7
21 42 63 105
The missing number in Sequence 2 is 780.
To find the missing number in Sequence 2, let's analyze the pattern:
In Sequence 1, the numbers increase by 1 each time: 126, 127, 128, 129, ...
In Sequence 2, the numbers seem to follow a pattern where each number is obtained by multiplying the corresponding number in Sequence 1 by a certain factor:
2 x 126 = 252
3 x 127 = 381
4 x 128 = 512
5 x 129 = 645
...
Looking at this pattern, we can see that the missing number in Sequence 2 should be:
6 x 130 = 780
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Your paycheck this week is $241. You put the $114 in a savings account that pays an interest
rate of 3.9%. If you leave your money for 2 years, how much will you have?
Answer:
$122.9
Step-by-step explanation:
Given data
Principal= $114
Rate= 3.9%
Time= 2 years
The amount in the account is given as
A=P(1+rt)
substitute
A=114(1+0.039*2)
A=114(1+0.078)
A=114(1.078)
A=$122.9
It costs $16 dollars each day to run an ad in the newspaper. You advertise for 8 days. How much did you spend on advertising?
A flagpole casts a shadow that is 14 feet long. At the same time, a person standing nearby who is 5 feet 6 inches tall casts a shadow
that is 42 inches long. How tall is the flagpole?
Flagpole:
feet
Answer:
22 feet
Step-by-step explanation:
As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:
14 ft = 14 × 12 = 168 inches5 ft 6 in = 5 × 12 + 6 = 66 inchesTherefore:
Flaghole height = h inFlagpole shadow = 168 inPerson height = 66 inPerson shadow = 42 inDraw a diagram using the given information (see attachment).
From the diagram, we can see that the flagpole and the person are parallel. Therefore, the two triangles are similar.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, set up a ratio of height to shadow length and solve for h:
\(\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow\)
\(\implies \sf h:168=66:42\)
\(\implies \sf \dfrac{h}{168}=\dfrac{66}{42}\)
\(\implies \sf h=\dfrac{66}{42} \cdot 168\)
\(\implies \sf h=\dfrac{11088}{42}\)
\(\implies \sf h=264\;inches\)
Convert the height into feet by dividing by 12:
\(\implies \sf h=\dfrac{264}{12}=22\;feet\)
Therefore, the height of the flagpole is 22 feet.
Write a numerical expression to represent the phrase "the sum of 25 and the cube of 9." Do not evaluate the expression.
Answer:
25 + 9^3
Step-by-step explanation:
Mark decided to make Christmas presents for his classmates. He bought 10 lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 per pound.
Write a function f(x) that represents the total cost of the candy, where x is the weight of the less expensive candy.
Total cost of the candy is represented by the function f (x) is;
⇒ f (x) = $2.80x + $3.50y
Where, x is the weight of the less expensive candy (caramel candy)
and, y is the weight of chocolate candies.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Mark bought 10 lb of two types of candies to make Christmas present for his classmates.
Let x is the weight of the less expensive candy (caramel candy).
And, y is the weight of chocolate candies.
Now, The cost of caramel candies = $2.80x
And, The cost of chocolate candies = $3.50y
Hence, Total cost of the candy = $2.80x + $3.50y
Therefore, Total cost of the candy is represented by the function f (x) is;
⇒ f (x) = $2.80x + $3.50y
Where, x is the weight of the less expensive candy (caramel candy)
and, y is the weight of chocolate candies.
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A class contains 5 girls and 7 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.
Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.
Determine the total number of students in the class. That is 5 + 7 = 12.
Determine the number of ways to select two students from the class.
Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.
In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).
C(12, 2) = 12! / (2!(12-2)!) = 66.
Determine the number of favorable outcomes.
In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.
To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):
Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.
So, the probability of selecting a girl and a boy for the class committee is 5/6.
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The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4.
The required graph is attached.
What is a graph?An organized representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
The modification looks like this.
Combining two transformations results in the transformation of
h(x) to -h(x) -4.
1. An X-axis-centered reflection. Every point (x, y) in h(x) is transformed into (x', y'), where x' = x and y' = -y. Hence, (x, y) (x, -y)
2. A 4-unit translation of each reflected point, where the x value remains constant, but the y value is translated downward to become y'-4 = -y -4
Every coordinate (x, y) in h(x) will be transformed to the following as a result of both transformations: (x, -y -4)
Given that the graph is made up of two straight lines that intersect at the origin, all we need to do is select any three points in h(x), determine their transformed coordinates, and then connect them using straight lines: h(x0 -h(X) - 4 (-2, 4) (-2, -4-4) =(-2, -8) (0, 0) (0, -0 - 4) =(0, -4) (4, 2) (4, (4, -6)
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a water tank is used to store water for livestock is in the shape of a cylinder with a diameter of 5 feet and a hight of 6 feet. the tank has sprung a leak. it is leaking water at a rate of 0.75 cubic feet per hour. if the tank is full how long should it take for the tank to empty
ANSWER
\(157.08\text{ hours}\)EXPLANATION
First, we have to find the volume of the cylindrical tank.
The volume of a cylinder is given as:
\(V=\pi\cdot r^2\cdot h\)where r = radius; h = height
We are given the diameter of the tank (5 feet). Radius is half of the diameter, so:
\(\begin{gathered} r=\frac{D}{2} \\ r=\frac{5}{2} \\ r=2.5ft \end{gathered}\)Therefore, the volume of the tank is:
\(\begin{gathered} V=\pi\cdot2.5^2\cdot6 \\ V=117.81ft^3 \end{gathered}\)The tank is leaking water at a rate of 0.75 ft³ per hour.
To find the time it will take for the tank to be empty, we have to divide the volume of the tank by the rate at which it is leaking.
That is:
\(\begin{gathered} \text{Time}=\frac{117.81}{0.75} \\ \text{Time}=157.08\text{ hours} \end{gathered}\)That is the time it will take for the tank to be empty.
4. What is the value of the underlined digit?
4,506,204,395.9812
The underlined digit being 8
Answer:
hundreth, because it is the second digit after the decimal point.
A woman is 42years old. Her daughter is 1/3 of her age. Three years ago the sum of her age was
Answer:
50
Step-by-step explanation:
So we know that 42/3=14.
3 years before was:
14-3=11
42-3=39
The sum of 11+39 is 50
If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
A restaurant customer left $1.95as a tip. The tax was 7% and the tip was %15 of the after tax cost. Which information is not needed to compute the bill after tax and tip? What was the total bill?
how do i solve 1-(1+.04/12)^-12x10
To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.
Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).
Step 3: Add 1 to 0.0033333 to get 1.0033333.
Step 4: Raise 1.0033333 to the power of -120.
Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.
Step 6: Subtract the value obtained in Step 5 from 1.
1 - 0.742657 = 0.257343 (approximately).
Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.
It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.
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8xn=24x7 what is the missing number?
Answer:
21
Step-by-step explanation:
24 x 7 = 168
168 / 8 = 21
8 x 21 = 168
168 = 168
Answer: 21
You would find this by multiplying the problem you know 24x7 which equals 168.8xn=24x7 which means, 8xn=168. So you would have to divide 168 by 8 n=21